Computation And Proof Theory

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Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification

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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2021-07-27

Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-27 with Mathematics categories.

This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.

Proceedings Of The Logic Colloquium Held In Aachen July 18 23 1983

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Author : M. M. Richter
language : en
Publisher: Springer
Release Date : 1984-12-01

Proceedings Of The Logic Colloquium Held In Aachen July 18 23 1983 written by M. M. Richter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-12-01 with Mathematics categories.

Proceedings Of The Logic Colloquium Held In Aachen July 18 23 1983

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Author : M. M. Richter
language : en
Publisher: Springer
Release Date : 2006-12-08

Proceedings Of The Logic Colloquium Held In Aachen July 18 23 1983 written by M. M. Richter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

Computation And Proof Theory

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Author : Michael M. Richter
language : en
Publisher: Springer
Release Date : 1984

Computation And Proof Theory written by Michael M. Richter and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

Concepts Of Proof In Mathematics Philosophy And Computer Science

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Author : Dieter Probst
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-07-25

Concepts Of Proof In Mathematics Philosophy And Computer Science written by Dieter Probst and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Philosophy categories.

A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.

Proofs And Computations

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Author : Helmut Schwichtenberg
language : en
Publisher: Cambridge University Press
Release Date : 2011-12-15

Proofs And Computations written by Helmut Schwichtenberg and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-15 with Mathematics categories.

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11-CA0. Ordinal analysis and the (Schwichtenberg-Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11-CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.

Advances In Proof Theory

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Author : Reinhard Kahle
language : en
Publisher: Birkhäuser
Release Date : 2016-05-04

Advances In Proof Theory written by Reinhard Kahle and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-04 with Mathematics categories.

The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. ​Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science.

Proof Theory In Computer Science

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Author : Reinhard Kahle
language : en
Publisher: Springer
Release Date : 2003-06-30

Proof Theory In Computer Science written by Reinhard Kahle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-30 with Computers categories.

Proof theory has long been established as a basic discipline of mathematical logic. It has recently become increasingly relevant to computer science. The - ductive apparatus provided by proof theory has proved useful for metatheoretical purposes as well as for practical applications. Thus it seemed to us most natural to bring researchers together to assess both the role proof theory already plays in computer science and the role it might play in the future. The form of a Dagstuhl seminar is most suitable for purposes like this, as Schloß Dagstuhl provides a very convenient and stimulating environment to - scuss new ideas and developments. To accompany the conference with a proc- dings volume appeared to us equally appropriate. Such a volume not only ?xes basic results of the subject and makes them available to a broader audience, but also signals to the scienti?c community that Proof Theory in Computer Science (PTCS) is a major research branch within the wider ?eld of logic in computer science.

Computational Logic And Proof Theory

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Author : Georg Gottlob
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-13

Computational Logic And Proof Theory written by Georg Gottlob and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-13 with Computers categories.

This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.

Computation And Proof Theory

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Author : Michael M. Richter
language : en
Publisher:
Release Date : 1984

Computation And Proof Theory written by Michael M. Richter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.